Struct MercatorBaseProjection 

pub struct MercatorBaseProjection<const C: i64> { /* private fields */ }

Mercator Projection

The Mercator projection is a cylindrical map projection originating from the 16th century. It is widely recognized as the first regularly used map projection. It is a conformal projection where the equator projects to a straight line at constant scale. A rhumb line, or course of constant heading, projects to a straight line, making it suitable for navigational purposes.

Classification: Conformal cylindrical

Available forms: Forward and Inverse, spherical and ellipsoidal

Defined area: Global, but best used near the equator

Alias: merc

Domain: 2D

Input type: Geodetic coordinates

Output type: Projected coordinates

Projection String

+proj=merc

Usage

The Mercator projection is often used for equatorial regions and navigational charts. It is not suitable for world maps due to significant area distortions. For example, Greenland appears larger than South America in the projection, despite Greenland’s actual area being approximately one-eighth of South America’s.

Examples:

• Using latitude of true scale:

  $ echo 56.35 12.32 | proj +proj=merc +lat_ts=56.5
  3470306.37    759599.90

• Using scaling factor:

  $ echo 56.35 12.32 | proj +proj=merc +k_0=2
  12545706.61    2746073.80

Note: +lat_ts and +k_0 are mutually exclusive. If both are used, +lat_ts takes precedence over +k_0.

Parameters

• lat_ts: Latitude of true scale
• k_0: Scaling factor
• lon_0: Longitude of origin
• x_0: False easting
• y_0: False northing
• ellps: Ellipsoid
• R: Radius of the sphere

Mathematical Definition

Spheroidal Form

• Forward Projection: $$x = k_0 \cdot R \cdot \lambda$$ $$y = k_0 \cdot R \cdot \psi$$ where $$\psi = \ln\left(\tan\left(\frac{\pi}{4} + \frac{\phi}{2}\right)\right)$$
• Inverse Projection: $$\lambda = x / (k_0 \cdot R)$$ $$\psi = y / (k_0 \cdot R)$$ $$\phi = \frac{\pi}{2} - 2 \cdot \arctan\left(\exp(-\psi)\right)$$

Ellipsoidal Form

• Forward Projection: $$x = k_0 \cdot a \cdot \lambda$$ $$y = k_0 \cdot a \cdot \psi$$ where $$\psi = \ln\left(\tan\left(\frac{\pi}{4} + \frac{\phi}{2}\right)\right) - 0.5 \cdot e \cdot \ln\left(\frac{1 + e \cdot \sin(\phi)}{1 - e \cdot \sin(\phi)}\right)$$
• Inverse Projection: $$\lambda = x / (k_0 \cdot a)$$ $$\psi = y / (k_0 \cdot a)$$ $$\phi = \arctan(\tau)$$ where $$\tau = \tan(\phi)$$

Further Reading

• Wikipedia: Mercator Projection
• Wolfram Mathworld: Mercator Projection

Trait Implementations

impl<const C: i64> Clone for MercatorBaseProjection<C>

fn clone(&self) -> MercatorBaseProjection<C>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<const C: i64> CoordinateStep for MercatorBaseProjection<C>

fn new(proj: Rc<RefCell<Proj>>) -> Self

Create a new Converter

fn forward<P: TransformCoordinates>(&self, p: &mut P)

forward conversion

fn inverse<P: TransformCoordinates>(&self, p: &mut P)

inverse conversion

impl<const C: i64> Debug for MercatorBaseProjection<C>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<const C: i64> PartialEq for MercatorBaseProjection<C>

fn eq(&self, other: &MercatorBaseProjection<C>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<const C: i64> ProjectCoordinates for MercatorBaseProjection<C>

fn code(&self) -> i64

ESPG code for this projection

fn name(&self) -> &'static str

Projection name

fn names() -> &'static [&'static str]

Returns the list of canonical names for this projection. This is an associated function, similar to a static method.

fn datum_type() -> u8

get the datum type. Defaults to no datum

impl<const C: i64> StructuralPartialEq for MercatorBaseProjection<C>